Identifying Accurate Crack Initiation and Propagation Thresholds in Siliceous Siltstone and Limestone
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TECHNICAL NOTE
Identifying Accurate Crack Initiation and Propagation Thresholds in Siliceous Siltstone and Limestone Xiao‑Ping Zhang1,2 · Gen‑Gen Lv1,2 · Quan‑Sheng Liu1,2 · Shun‑Chuan Wu3,4 · Qi Zhang1,2 · Pei‑Qi Ji1,2 · Xu‑Hai Tang1,2 Received: 19 March 2019 / Accepted: 12 October 2020 © Springer-Verlag GmbH Austria, part of Springer Nature 2020
Keywords Crack initiation · Stress–strain curve · Stress thresholds · Acoustic emission monitoring List of Symbols σcc Crack closure stress σci Crack initiation stress σcd Crack damage stress σf Peak strength 𝜀v Volumetric strain 𝜀ve Elastic volumetric strain 𝜀vc Crack volumetric strain ΔV Change of specimen volume ΔVelastic Change of elastic volume 𝜀axial Axial strain 𝜀lateral Lateral strain E Elastic modulus ν Poisson’s ratio P wave Pressure wave 𝜎1 Maximum loading stress 𝜎3 Minimum loading stress Abbreviations AE Acoustic emission CVS Crack volumetric strain method * Xiao‑Ping Zhang [email protected] * Quan‑Sheng Liu [email protected] 1
Key Laboratory of Safety for Geotechnical and Structural Engineering of Hubei Province, School of Civil Engineering, Wuhan University, Wuhan 430072, China
2
State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, Hubei, China
3
Faculty of Land Resources Engineering, Kunming University of Science and Technology, Kunming, Yunnan 650093, China
4
School of Civil and Resource Engineering, University of Science and Technology Beijing, Beijing 100083, China
LSR Lateral strain response method MPR Moving point regression method
1 Introduction Deep buried tunnels often suffer brittle instability and failure during the excavation process under high geological stress conditions (Liu et al. 2018). During this process, the surrounding rocks partially begin to break with crack initiation and growth. The deformation and failure of brittle rocks is a gradual process involving the initiation, growth and aggregation of cracks (Martin and Chandler 1994). The deformation and failure process of brittle rocks has been widely concerned by many researchers (Dai et al. 2015; Yang 2016; Yang and Hu 2019; Yang et al. 2018; Zhang and Wong 2013; Zhang et al. 2017; Zhou et al.2015). Researchers studied the failure of brittle rocks and divided the stress–strain curves of brittle rocks into five stages: stage I-crack closure; stage II-linear elastic deformation; stage III-crack initiation and stable crack growth; stage IV-unstable crack growth; and stage V-failure and post-peak behavior (Wawersik and Brace 1971; Eberhardt et al. 1999; Hoek and Bieniawski 1965; Scholz 1968; Zhou et al. 2014; Cheng et al. 2016; Zhang et al. 2011; Hallbauer et al. 1973; Tapponnier and Brace 1976). These five stages of the stress–strain curve are divided by four stress thresholds: crack closure stress (σcc), crack initiation stress (σci), crack damage stress (σcd) and peak strength (σf). The crack closure stress (σcc) indicates the closing of the preexisting microcracks within the rock; the cra
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